Glossary: Improper Integrals

·         Improper Integral

An integral with at least one infinite limit or an unbounded integrand.

·         Infinite Interval

When one or both integration limits are infinite.

·         Infinite Discontinuity

When the integrand becomes infinite at some point of the interval.

·         Convergent Integral

An improper integral that has a finite limit.

·         Divergent Integral

An improper integral that does not have a finite limit.

·         Limit Definition

Improper integrals are defined by limits replacing infinite bounds or singularities.

·         p-Test

The integral ∫₁^∞ (1/x^p) dx converges if p > 1 and diverges if p ≤ 1.

·         Asymptotic Behavior

Describes how a function behaves as x → ∞ or near a singularity.

·         Comparison Test

A method to determine convergence by comparing with a known convergent or divergent integral.